On the variance of the number of occupied boxes

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

34 pages

Scientific paper

We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its variance V_n tends to infinity. In this work, we mainly focus on the opposite case where V_n is bounded, and derive a simple necessary and sufficient condition for convergence of V_n to a finite limit, thus settling a long-standing question raised by Karlin in the seminal paper of 1967. One striking consequence of our result is that the possible limit may only be a positive integer number. Some new conditions for other types of behavior of the variance, like boundedness or convergence to infinity, are also obtained. The proofs are based on the poissonization techniques.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On the variance of the number of occupied boxes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the variance of the number of occupied boxes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the variance of the number of occupied boxes will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-648340

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.